1. Field of the Invention
The present invention relates to a method for modelling steady and transient flows, in pipes, of a mixture of multiphase fluids.
2. Description of the Prior Art
It is well-known that the flow modes of multiphase fluids in tubes are extremely varied and complex. Two-phase flows for example can be stratified, the liquid phase flowing through the lower part of the pipe, or intermittent with a succession of liquid and gas slugs, or dispersed, the liquid being carried in the form of fine droplets. The flow mode varies notably with the slope of the pipes with respect to the horizontal and it depends on the flow rate of the gas phase, on the temperature, etc. The slippage between the phases, which varies according to whether the ascending or descending portions are considered. leads to pressure variations without there being compensation. The characteristics of the flow pattern (dimensioning, pressure, gas flow rate, etc.) must be carefully determined.
Examples of the many publications focused on the behaviour of flows, notably two-phase flows, in pipes are:
Fabre J. et al, 1983, Intermittent Gas-Liquid Flow in Horizontal or Slightly Inclined Pipes, Int. Conference on the Physical Modelling of Multi-Phase Flow, Coventry, England, p.233-254, or
Fabre J. et al, 1989, Two Fluid/Two Flow Pattern Model for Transient Gas Liquid Flow In Pipes, Int. Conference on Multi-Phase Flow, Nice, France; P269-284, Cranfield, BHRA.
An existing modeling method deals with phase chances by iterative processes. The state of the mixture is supposed to be known a priori and if this leads to inconsistencies after hydrodynamic calculations, the calculations are repeated with a new state of the mixture. This method requires considerable processing and can be the source of convergence problems.
A modeling method applied to porous media is described for example by Eymard R., Gallouet T., 1991, Traitement des Changements de Phases dans la Modelisation de Gisements Petroliers, Journees Numeriques de Besancon, 23-24 September 1991.
U.S. Pat. No. 5,550,761 describes a method for modeling steady or transient multiphase flows that accounts for a set of variables defining the properties of the fluids and of the flow modes, and also of the dimensions and the slopes of the feed pipes. The quantities characterizing the flow are determined by solving a set of transport equations with an equation of mass conservation per phase and an equation of momentum of the mixture, and by using a hydrodynamic model and a thermodynamic characteristic of the fluids.
To obtain this hydrodynamic model, the flow regimes are characterized by a parameter ranging between 0 and 1 and representative of the fraction of the flow that is in a separate state (the phases are stratified vertically or radially for example), any flow regime is determined while solving the transport equations by comparing the current value of the liquid fraction in the slugs and that of the areas with a dispersed flow mode, the velocity of the slugs of the gas phase are also determined with respect to a critical velocity, and continuity constraints are imposed on the boundaries between regimes, on the gas volume fractions and on the slug displacement velocity during solution of closing relations.
In the previous method, an approach "by phase" (liquid-gas) was selected where mass conservation is expressed by an equation of conservation per phase and mass transfer between phases is expressed by an imbalance term proportional to the difference between two vapour mass fraction values, one fmva.sub.eq corresponding to equilibrium, which is provided by thermodynamics with a constant global composition, the other being calculated by taking account of the slippage between the phases ##EQU1## where AGKL is a factor depending a priori on the fluid and on the flow pattern.
It has been noticed with practice that it is difficult to define a formulation of this imbalance term which applies to all situations: local slopes of pipes with upper and lower points, considerable mass transfers between phases. There is no reliable and robust method which correctly accounts for the imbalance term between phases; the liquid-gas approach "by phase" gives no satisfactory results in cases where considerable transfers occur between phases.